I have low hanging ductwork that is framed in with 1" of clearance (they used metal RC strapping). It's against a wall in an area that needs some lighting. Does such a solution exist where recessed lights are less than 1.5" (0.5" for drywall) deep?

Originally I planned on using LED lights, but all that is nearby is the light switch box (drywall up the walls, ceiling, etc). I have nowhere to put a transformer, unless I'm allowed to slip it up with the lights, and that assumes it's 1" thick.

Thoughts?